Question

Find the number of positive integers not satisfying the inequality
[
begin{array}{r}
log _{2}left(4^{x}-2.2^{x}+17right)>5
4^{x}-2 cdot 2^{x}+17=left(2^{x}right)^{2}-2 cdot 2^{x}+1+16
=left(2^{x}-1right)^{2}+16>0
end{array}
]
the condition ( 4^{x}-22^{x}+17>0 ) is satufret for any real ( x )
( log _{2}left[left(2^{x}-1right)^{2}+16right]>5 Rightarrowleft(2^{x}-1right)^{2}+16>2^{5} )
[
begin{array}{l}
left(2^{x}right)^{2}+16>32
left(2^{x}-1right)^{2}>16
end{array}
]

# "wy 091/ 5 20 F-3. Find the number of positive integers not satisfying the inequality log (4x - 2.2 + 17) > 5. F-4. Solve the following inequalities :

Solution